{"id":"https://openalex.org/W2168856522","doi":"https://doi.org/10.37236/184","title":"Hurwitz Equivalence in Tuples of Dihedral Groups, Dicyclic Groups, and Semidihedral Groups","display_name":"Hurwitz Equivalence in Tuples of Dihedral Groups, Dicyclic Groups, and Semidihedral Groups","publication_year":2009,"publication_date":"2009-08-07","ids":{"openalex":"https://openalex.org/W2168856522","doi":"https://doi.org/10.37236/184","mag":"2168856522"},"language":"en","primary_location":{"id":"doi:10.37236/184","is_oa":true,"landing_page_url":"https://doi.org/10.37236/184","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r95/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r95/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057752944","display_name":"Charmaine Sia","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Charmaine Sia","raw_affiliation_strings":["Department of Mathematics Massachusetts Institute of Technology Cambridge, MA 02139-4307, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Massachusetts Institute of Technology Cambridge, MA 02139-4307, USA","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057752944"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.9469,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.73704216,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"16","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10304","display_name":"Geometric and Algebraic Topology","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12037","display_name":"Algebraic and Geometric Analysis","score":0.9905999898910522,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dihedral-group","display_name":"Dihedral group","score":0.9270917177200317},{"id":"https://openalex.org/keywords/dicyclic-group","display_name":"Dicyclic group","score":0.8273633718490601},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7226483821868896},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7219666242599487},{"id":"https://openalex.org/keywords/beta","display_name":"BETA (programming language)","score":0.6640986204147339},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6190301179885864},{"id":"https://openalex.org/keywords/group","display_name":"Group (periodic table)","score":0.5821343064308167},{"id":"https://openalex.org/keywords/alpha","display_name":"Alpha (finance)","score":0.48109811544418335},{"id":"https://openalex.org/keywords/equivalence-relation","display_name":"Equivalence relation","score":0.4511033594608307},{"id":"https://openalex.org/keywords/dihedral-angle","display_name":"Dihedral angle","score":0.423494815826416},{"id":"https://openalex.org/keywords/cyclic-group","display_name":"Cyclic group","score":0.4099828004837036},{"id":"https://openalex.org/keywords/non-abelian-group","display_name":"Non-abelian group","score":0.20947885513305664},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.12640470266342163},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0518898069858551}],"concepts":[{"id":"https://openalex.org/C72409365","wikidata":"https://www.wikidata.org/wiki/Q558339","display_name":"Dihedral group","level":3,"score":0.9270917177200317},{"id":"https://openalex.org/C130630368","wikidata":"https://www.wikidata.org/wiki/Q3777914","display_name":"Dicyclic group","level":5,"score":0.8273633718490601},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7226483821868896},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7219666242599487},{"id":"https://openalex.org/C2776174256","wikidata":"https://www.wikidata.org/wiki/Q830842","display_name":"BETA (programming language)","level":2,"score":0.6640986204147339},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6190301179885864},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.5821343064308167},{"id":"https://openalex.org/C64943373","wikidata":"https://www.wikidata.org/wiki/Q2651003","display_name":"Alpha (finance)","level":4,"score":0.48109811544418335},{"id":"https://openalex.org/C156103551","wikidata":"https://www.wikidata.org/wiki/Q130998","display_name":"Equivalence relation","level":2,"score":0.4511033594608307},{"id":"https://openalex.org/C89025888","wikidata":"https://www.wikidata.org/wiki/Q911907","display_name":"Dihedral angle","level":4,"score":0.423494815826416},{"id":"https://openalex.org/C20725272","wikidata":"https://www.wikidata.org/wiki/Q245462","display_name":"Cyclic group","level":3,"score":0.4099828004837036},{"id":"https://openalex.org/C170124329","wikidata":"https://www.wikidata.org/wiki/Q592651","display_name":"Non-abelian group","level":4,"score":0.20947885513305664},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.12640470266342163},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0518898069858551},{"id":"https://openalex.org/C136170076","wikidata":"https://www.wikidata.org/wiki/Q181296","display_name":"Abelian group","level":2,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C32909587","wikidata":"https://www.wikidata.org/wiki/Q11369","display_name":"Molecule","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C171606756","wikidata":"https://www.wikidata.org/wiki/Q506132","display_name":"Psychometrics","level":2,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C112887158","wikidata":"https://www.wikidata.org/wiki/Q169324","display_name":"Hydrogen bond","level":3,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C49453240","wikidata":"https://www.wikidata.org/wiki/Q1592163","display_name":"Construct validity","level":3,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/184","is_oa":true,"landing_page_url":"https://doi.org/10.37236/184","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r95/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.214.3012","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.3012","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_16/PDF/v16i1r95.pdf","raw_type":"text"},{"id":"pmh:oai:dspace.mit.edu:1721.1/89810","is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/89810","pdf_url":null,"source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Electronic Journal of Combinatorics","raw_type":"http://purl.org/eprint/type/JournalArticle"}],"best_oa_location":{"id":"doi:10.37236/184","is_oa":true,"landing_page_url":"https://doi.org/10.37236/184","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r95/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G264516904","display_name":null,"funder_award_id":"H98230-06-1-001","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G5921281487","display_name":null,"funder_award_id":"number","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6507447573","display_name":null,"funder_award_id":"several","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6986451848","display_name":null,"funder_award_id":"DMS 0754106","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7587565994","display_name":"REU Site: An undergraduate research program in Discrete Mathematics","funder_award_id":"0754106","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7845798442","display_name":null,"funder_award_id":"H98230","funder_id":"https://openalex.org/F4320311089","funder_display_name":"National Security Agency"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320309369","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44"},{"id":"https://openalex.org/F4320309636","display_name":"University of Minnesota","ror":"https://ror.org/03grvy078"},{"id":"https://openalex.org/F4320311089","display_name":"National Security Agency","ror":"https://ror.org/0047bvr32"},{"id":"https://openalex.org/F4320311500","display_name":"University of Minnesota Duluth","ror":"https://ror.org/01hy4qx27"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2168856522.pdf","grobid_xml":"https://content.openalex.org/works/W2168856522.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W2016113260","https://openalex.org/W2018614037","https://openalex.org/W2102603366","https://openalex.org/W2152651756","https://openalex.org/W2949309105","https://openalex.org/W4299921512"],"related_works":["https://openalex.org/W4313642480","https://openalex.org/W2102603366","https://openalex.org/W3007814923","https://openalex.org/W4251070131","https://openalex.org/W4362598299","https://openalex.org/W4387323450","https://openalex.org/W2053651143","https://openalex.org/W2030503921","https://openalex.org/W2334694979","https://openalex.org/W2077048433"],"abstract_inverted_index":{"Let":[0],"$D_{2N}$":[1],"be":[2],"the":[3,11,18,26,50,60],"dihedral":[4],"group":[5,13,20,27],"of":[6,14,21,28],"order":[7,15,22,29],"$2N$,":[8],"${\\it":[9,54],"Dic}_{4M}$":[10],"dicyclic":[12],"$4M$,":[16],"$SD_{2^m}$":[17],"semidihedral":[19],"$2^m$,":[23],"and":[24,57],"$M_{2^m}$":[25],"$2^m$":[30],"with":[31],"presentation":[32],"$$M_{2^m}":[33],"=":[34,40,42,45],"\\langle":[35],"\\alpha,":[36],"\\beta":[37],"\\mid":[38],"\\alpha^{2^{m-1}}":[39],"\\beta^2":[41],"1,\\":[43],"\\beta\\alpha\\beta^{-1}":[44],"\\alpha^{2^{m-2}+1}":[46],"\\rangle.$$":[47],"We":[48],"classify":[49],"orbits":[51],"in":[52],"$D_{2N}^n$,":[53],"Dic}_{4M}^n$,":[55],"$SD_{2^m}^n$,":[56],"$M_{2^m}^n$":[58],"under":[59],"Hurwitz":[61],"action.":[62]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}